Asahina was born in Tokyo as an illegitimate child of Kaichi Watanabe. He founded the Kansai Symphonic Orchestra (today the Osaka Philharmonic Orchestra) in 1947 and remained its chief conductor until his death in Kobe. Inspired by a meeting with Wilhelm Furtwängler in the 1950s, he began a lifelong attachment to the music of Anton Bruckner, recording the complete Bruckner symphonies several times. For many years, he was associated with the North German Radio Orchestra in Hamburg. Towards the end of his life, he made several appearances with the Chicago Symphony Orchestra.